You need to show your work so we can see where you could be making errors. Expanding and grouping terms in that equation should not lead to a complete mess. Don't worry about isolating v1f, you can't do it directly anyway*. Just show what you get when you expand and simplify that expression...
It seems that you are hung up on a "have no numbers" thing and it is preventing you from trying the question. No numbers are required.
These are your equations from the posts you wrote:
3v = 3v1f + v2f
3(v1i)^2 = 3(v1f)^2 + (v2f)^2
One thing I notice is that you weren't consistent in...
You don't need to know the actual values. You have two equations that are related by the same variables, you can combine them and come up with an expression for the final velocity of the 3m mass.
You are on the right track but the red part is not quite correct. Remember that once the man starts moving, the flatcar is no longer going at 16.8 m/s. How does that change your equation?
Since I don't know what the other question was, I can't tell you what's different. You need to do vector components because the point of interest is not on the same line as the two charges. It is a two dimensional situation. Have you tried what I suggested?
Is the question asking you to find the actual period? Because the data you show is the time it takes the pendulum to go 15 swings, not one (which is what the period would be).
Am I misreading what you've written?